In a large pot of boiling, salted water, cook the corn until the kernels are crisp-tender, about 5 minutes. Remove from the pot using tongs.

Peel back each cob's husk, then use one strand to tie it together; discard the silk. Grill the corn over medium heat, turning occasionally, until tender and browned in spots, 12 to 15 minutes. In a food processor, puree 1/2 cup mayo with 1 canned chipotle in adobo sauce; slather on the corn. Sprinkle with cotija cheese; serve with lime wedges.